基于事件触发和状态翻转的布尔控制网络输出跟踪

利用矩阵半张量积研究事件触发和翻转控制共同作用下布尔控制网络的输出跟踪问题.首先,基于布尔控制网络代数状态空间表示,构造增广系统将输出跟踪问题转化为状态集镇定问题;其次,得到布尔控制网络在两种控制下输出跟踪问题有解的充要条件,并在满足该条件时提出一种基于最小翻转节点集时间最优控制设计方法,进一步给出有限时间内寻找翻转节点集的计算过程;最后,给出一个算例说明结果的可行性.     

布尔控制网络的输出稳定与镇定

矩阵的半张量积是将逻辑变量转化为向量研究的主要工具.本文利用半张量积把逻辑控制系统表示为离散时间仿射线性系统,在逻辑系统的状态空间框架下研究了以布尔控制网络为代表的逻辑动态系统的输出稳定与镇定.首先给出布尔网络输出稳定的定义,研究了布尔网络输出稳定的充要条件;其次讨论了布尔控制网络的输出镇定,分别得到了布尔控制网络由常值输入变量、自由控制序列、状态反馈控制序列输出镇定的条件.本文讨论的系统输出稳定与镇定是(部分)变量稳定与镇定的推广.     

受扰布尔控制网络全局可重构分析与状态估计

受扰布尔控制网络的状态转移,因受未知干扰影响而具有不确定性,这对状态观测器设计带来了困难.本文主要研究了受扰布尔控制网络全局可重构性问题,并在此基础上设计状态观测器.首先,将受扰布尔控制模型转化为多个子系统的切换未知布尔控制网络模型,在此基础上,提出了受扰布尔控制网络的4种不同状态集.其次,基于状态集估计方法,对受扰布尔控制网络状态估计问题进行分析.再次,提出有限时间可重构与全局可重构性概念;同时,根据状态集估计与状态转移分析,分别给出有限时间可重构判定算法与全局可重构性证明的充要条件.最后,给出观测器设计方法,并通过例子证明了本文提出方法的可行性.     

基于牵制控制的切换布尔网络的分布式集合镇定

切换布尔网络是一种典型的网络化控制系统, 在基因调控、信息安全、人工智能、电路设计等领域具有重 要应用. 本文基于牵制控制方法, 研究切换布尔网络在任意切换下的分布式集合镇定问题. 首先, 利用矩阵半张量积 方法,得到切换布尔网络的代数形式. 其次, 基于代数形式, 提出构造性的算法来实现切换布尔网络在牵制控制的 作用下任意切换集合镇定, 并设计出状态反馈牵制控制器. 再次, 利用逻辑矩阵分解技术和分布式控制方法, 设计任 意切换下切换布尔网络的分布式集合镇定控制器, 并提出分布式控制器存在的充分条件. 文中给出3个例子来说明 所获得结果的有效性.     

概率布尔控制网络的弱能控性

本文研究了概率布尔控制网络的弱能控性,系统的弱能控性是概率布尔网络精确能控的一个推广.首先利用矩阵的半张量积和逻辑变量的向量表示,概率布尔控制网络被表示为离散时间动态系统.接着给出概率布尔控制网络弱能控的定义,从离散时间系统的结构矩阵出发,构造了最大概率转移矩阵,矩阵中的元素表示相应状态之间可能发生转移的最大概率,在此基础上研究了概率布尔控制网络的弱能控的条件,同时给出了两个状态弱能达时控制序列的设计算法.最后通过例子进一步解释了弱能控的概念和控制序列设计算法的有效性.     

概率布尔控制网络的集可控

本文研究概率布尔控制网络的集可控性问题.首先,利用矩阵半张量积方法,得到概率布尔控制网络的代数表示.其次,借助一个新的算子构造不同的可控矩阵,进而通过可控矩阵考虑自由控制序列和网络输入控制下概率布尔控制网络的集可控性问题,得到了概率布尔控制网络集可控性的充要条件.最后,给出数值例子说明本文结果的有效性.     

概率级联布尔网络的集镇定及其应用

随着系统生物学和医学的迅速发展,基因调控网络已经成为一个热点研究领域.布尔网络作为研究生物系统和基因调控网络的一种重要模型,近年来引起了包括生物学家和系统科学家在内的很多学者的广泛关注.本文利用代数状态空间方法,研究了概率级联布尔网络的集镇定问题.首先给出概率级联布尔网络集镇定的定义,并利用矩阵的半张量积给出了概率级联布尔网络的代数表示.其次基于该代数表示,定义了一组合适的概率能达集,并给出了概率级联布尔网络集镇定问题可解的充要条件.最后将所得的理论结果应用于概率级联布尔网络的同步分析及n人随机级联演化布尔博弈的策略一致演化行为分析.     

状态和输入受限的切换奇异布尔控制网络的最优控制

本文研究了状态和输入均受限的切换奇异布尔控制网络的最优控制问题.利用矩阵半张量积方法获得受限切换奇异布尔控制网络的等价代数形式.然后通过类似针变化得到了存在最优控制的必要条件,并且提出了一个算法设计切换序列和控制策略使收益函数最大化.最后给出例子验证所得结果的有效性.     

基于容许集的变终端约束MPC控制

针对一类输入和状态受约束的离散线性系统,提出一种基于Ⅳ步容许集的变终端约束集模型预测控制方法.首先给出多面体不变集序列作为终端约束集的离线模型预测控制算法,扩大了终端约束集.为进一步扩大初始状态可镇定区域,引入N步容许集,设计了基于容许集的变终端约束集模型预测控制方法.该算法采用离线设计、在线优化方法,实现了系统渐近稳定,不仅降低了在线运算量,而且扩大了初始状态可镇定区域.仿真结果表明了算法的有效性.     

状态和输入受限的切换奇异布尔控制网络的最优控制（英文）

本文研究了状态和输入均受限的切换奇异布尔控制网络的最优控制问题.利用矩阵半张量积方法获得受限切换奇异布尔控制网络的等价代数形式.然后通过类似针变化得到了存在最优控制的必要条件,并且提出了一个算法设计切换序列和控制策略使收益函数最大化.最后给出例子验证所得结果的有效性.     

Controllability and stabilization of Boolean control networks by the auxiliary function of flipping

In this article, a hybrid method combining flip matrix approach and an open (or closed) loop control is proposed to study global controllability and stabilization of Boolean control networks (BCNs). First, the necessary and sufficient condition for global controllability of BCNs, by flipping some members of a perturbation set and under free control sequences, is proposed. After that, using a search algorithm, the minimal perturbation sets for global controllability (MS‐GCs) of the BCN are obtained. Next, we propose a necessary and sufficient criterion for global stabilization of BCNs by flipping some members of a perturbation set and under a state feedback control. Similarly, an algorithm is given to search for the minimal perturbation sets for global stabilization (MS‐GSs) of the BCN. Moreover, the time‐optimal MS‐GSs of the BCN are also obtained by an algorithm. Some examples are given to illustrate the effectiveness of the results.     

An average optimal control approach to the set stabilization problem for boolean control networks

This paper addresses the set stabilization problem for deterministic Boolean control networks (BCNs). An optimal control approach is investigated to solve the problems by using the semi‐tensor product of matrices, where a policy iteration algorithm for the set stabilization problem is deduced. Finally, the intervention problem of a cAMP receptor protein is addressed in the framework of the set stabilization problem. The problem is solved to validate the effectiveness of the proposed policy iteration approach for a practical application.     

On controllability and stabilizability of probabilistic Boolean control networks

The controllability of probabilistic Boolean control networks(PBCNs)is first considered.Using the input-state incidence matrices of all models,we propose a reachability matrix to characterize the joint reachability.Then we prove that the joint reachability and the controllability of PBCNs are equivalent,which leads to a necessary and sufcient condition of the controllability.Then,the result of controllability is used to investigate the stability of probabilistic Boolean networks(PBNs)and the stabilization of PBCNs.A necessary and sufcient condition for the stability of PBNs is obtained first.By introducing the control-fixed point of Boolean control networks(BCNs),the stability condition has finally been developed into a necessary and sufcient condition of the stabilization of PBCNs.Both necessary and sufcient conditions for controllability and stabilizability are based on reachability matrix,which are easily computable.Hence the two necessary and sufcient conditions are straightforward verifiable.Numerical examples are provided from case to case to demonstrate the corresponding theoretical results.     

Controllability of Boolean control networks with time delays in states

This paper investigates the controllability of Boolean networks with time-invariant delays in states. After a brief introduction on converting the logic dynamics to discrete time delay systems, the controllability via two kinds of controls is studied. One kind of control is generated by Boolean control networks, another kind of control is free Boolean sequences. In both cases, necessary and sufficient conditions of the controllability of Boolean control networks are proved. Finally, examples are given to illustrate the efficiency of the obtained results.     

Minimum time control of large‐scale boolean control networks with constraints

The minimum time control that steers a large‐scale Boolean control network with constraints from an initial state to a given state is investigated. This problem is studied under the partition of the large‐scale Boolean control networks. Based on that, the problem is converted to finding the minimum time control for each subnetwork. Hence, the minimum time control for small size Boolean control networks with constraints is considered firstly. Then, a method to solve the problem for large‐scale Boolean control networks with constraints is presented. Finally, a numerical example on T‐cell receptor kinetics is given to show the effectiveness of the main results.     

Feedback control and output feedback control for the stabilisation of switched Boolean networks

This paper presents the feedback control and output feedback control for the stabilisation of switched Boolean network. A necessary condition for the existence of a state feedback controller for the stabilisation of switched Boolean networks under arbitrary switching signal is derived first, and constructive procedures for feedback control and output feedback control design are provided. An example is introduced to show the effectiveness of this paper.     

Maximum lifetime rate control and random access in multi-hop wireless networks

Network lifetime and transmission quality are of paramount importance for rate control in an energy constrained multi-hop wireless network. It is known that they depend on mechanisms that span several protocol layers due to the existing interference across collision links and the energy constrained nature of wireless nodes. Although separate consideration of these issues simplifies the system design, it is often insufficient for wireless networks when the overall system performance is required. In this paper, we present a framework for cross-layer rate control towards maximum network lifetime and collision avoidance. The main contributions of this paper are twofold. First, although the link attainable rate is typically a non-convex and non-separable function of persistent probabilities, we prove the convergence of this cross-layer algorithm to the global optimum of joint congestion control and random access algorithm under the framework of nonlinear programming. Second, by adjusting a parameter in the objective function, we achieve the tradeoff between transmission quality and network lifetime. Simulations illustrate the desirable properties of the proposed algorithm, including convergence to the global optimum, better performance than the layered scheme, desirable tradeoff between transmission quality and network lifetime.